- Find the solution of the separable DE 2ydy = (x + 1)dx. a. y- +x x+c c y=x'+x+C d. y=x + 3x + C b. y=+

Q: If f(x, y) = 2x² – 8y², then the total differential of f at x = 1 and y = -2 is : - O df = 32 dx + 4…

A: In total differential take the derivative of each terms, put the given values and simplify.

Q: Obtain the general solution of y√(1+x^2)dx+ x√(1+ y²)dy = 0 using variable separable method.

A: solution is given below..

Q: What is the differential equation of the orthogonal trajectories of х3 — Зху — у3 — с? (1) (x+ y²)dx…

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Q: Solve the particular solution of the given DE: x(r^3-xy^2+2y^3 )dy-y(r^3+2y^3 )dx=0 @r=1, y=1. * O…

A: The particular solution of differential equation is the general solution without the integration…

Q: A particular solution of 4x² dy dx dy 4 is vx +8.x- +y = de

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Q: What is the differential equation of the orthogonal trajectories of х3 — Зху — у3 — с? (1) (x +…

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Q: Find the valve of k so that (2y sın x cos x -y + 2 y e** ) dx - (x - sın' x + kxye*) dy 0 becomes…

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Q: Find the general solution of dy – qy³ Py – dt by making a suitable substitution that transforms the…

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Q: Find the general solution of dy -my – ny³ dt by making a suitable substitution that transforms the…

A: Differential equation

Q: Find the general solution of 2x°eWx + x³y²_ y x*y x + y Сх— х In(x?), a) Oy= In x + y Сх- х In(x?),…

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Q: Obtain the General Solution of dx + xydy = y²dx + ydy.

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Q: Express the solution of the given initial value problem in terms of a convolution integral y" + 12y'…

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Q: Find the general solution of the following reducible second-order DE: x*y"+3.xy'= 2 Ans:…

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Q: The order of the differential equat 2x2 - 3+y = 0 dy + y = 0 dx2 dx O not defined O 2

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Q: 1. Consider the DE dy dz dy -5- + 4y = 8x + 2, y(0) = 1 dr Verify that y = Ae + 2x + 3 is a solution…

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Q: we solve thd DE y dx 2x0y-0aer convedding it to oad sing an integrating tactor, then the solution…

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Q: If f(x, y) = 4x² – 6y², then the total differential of f at x = 1 and y = -2 is : O df = 24 dx + 8…

A: df=dx+dy (see step 2).

Q: (b) Find the general integral of the partial differential equation dz dz. = 7., X- which contains…

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Q: Find the particular solution to DE:  ( xy^2 - x ) dx - ( 2x^2y - 3y ) dy = 0 ; y ( 1 ) = 2

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Q: The DE dy/dt = µy – oy², µ > 0 and o > 0 occurs in the study of population dynamics. It has general…

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Q: 2. Determine the solution of y? dt + (2yt + 1) dy = 0given that given that y (-1) = 8

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Q: Use the Euler method to solve d²y 0.5t + y = 0 dt2 where y (0) = 2 and y'(0) = 0. Solve from x = 0…

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Q: Q4: Find the general solution of d?y dy - 3 - 4y 3e2t + 2sin t - 8et cos 2t, dt dy y(0) = 2, (0) %3…

A: Given that  The differential equation  To find the general solution

Q: Ql: verify that the indicated pair of functions is a solution of the given system of differential…

A: Given equations are x=e-2t+3e6t and y=-e-2t+5e6t. Compute the derivative with respect to t.…

Q: Find the general solution of dy 3 -my – ny | dt

A: We need to find the general solution of the differential equation dydt=-my-ny3. The solution is…

Q: 2 dx + dy - ux -y set dt dメ + 3x +y=0 dt And the solution fone tlons xL+) ond y(+) of the line or…

A: Given differential equations are…

Q: (x² + 2xy – 4y²)dx – (x² – 8xy – 4y²)dy = 0 - %3D -

A: Consider (x2+2xy-4y2)dx-(x2-8xy-4y2)dy=0⇒ (x2+2xy-4y2)dx=(x2-8xy-4y2)dy⇒dydx=x2+2xy-4y2x2-8xy-4y2To…

Q: 6. Find the general solution to the DE. Show all of your work. dy =-0.2y+10 dt

A: Particular Differential Equation: A differential equation which is either in the form of , then the…

Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ? А)…

A: Find orthogonal trajectory

Q: 2. Variable Separable eyx a) dy =D dx ey+x?ey

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Q: 1. Show that the solution of: dy x? y 1.1 with initial condition , y(1) = 2 dx 1+ x3 is y = V4 +…

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Q: Find the general solution of the DE dy/dx = y(x – y) / x^2

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Q: 2. Find the particular solution of (xy + x)dx = (x?y² + x² + y² + 1)dy satisfying the initial…

A: Using Variable Separable Method

Q: 14. The particular integral of the differential dyd - 2y = e2x for some equation constents and u…

A: Using the method of undetermined coefficient

Q: Show that the DE (4y3 -6xy)dy = (3y2 +2x)dx is exact and find a solution of the IVP: (4y3 - 6xy)dy…

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Q: Find the general solution of the DE (x + y)dx + (x - y)dy =0.

A: Given differential equation is(x+y)dx+(x-y)dy=0Here, M=x+y and N=x-ythen ∂M∂y=1 and…

Q: find the general solution to the homogeneous DE [xsin(y/x)-ycos(y/x)]dx+xcos(y/x)dy=0

A: The solution is given as

Q: dr2 dx dx d²y, 7 dy , 9y 3. dr2 dy =1 at x = 1. dx = 0; y = 0 and x dx x2 4. Use the method of…

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Q: 2. Determine the solution of y dt + (2yt + 1) dy = 0given that given that y (-1) =Q

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Q: +z-y=3e' %3D dt dr dy + 2r+2y= e' dt dt

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Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y)=3x<y becomes dx dz 1 A…

A: Topic  =Differential equation Correct option  = A

Q: Find the general solution of the DE sec x dy = y dx. O In y = e^x +c O In y = sin x + c

A: Our Aim is to find the general solution of the differential equation given below:-sec (x) dy=y dx…

Q: Solve the Euler equation d²y dx dy -5y = 0 dx 31 d', 3x2 given that y(1) =1 and y'(1) = 2. intai

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Q: у" - Зу'- 4y %3D 2хe*

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Q: What is the integrating factor of the non-exact DE (4xy+3y²-x) dx + x(x+2y)dy =0 ? (A) x² 1 B (U) D…

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Q: Find the general solution of the DE dyldx = (x + y) / x. O y = (x^2)ln(Cx) O y = (x^3)ln(Cx) O y =…

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Q: Find the particular solution of the separable DE with the given boundary condition. e ; when x-0 and…

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Q: Consider a disease that propagates according to the system dx 3 357 — Зху — Зх dt - dy = X dt х*у —…

A: Given that, dxdt=357-3xy-3xdydt=x2y-13xy-68y The equilibrium points are,…

Q: Solve for the particular solution of the following non-homogeneous DE. y''-2y'=ex

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