Find the integral surface (general solution) of the differential equation2+-(*+y)z.dx4 Find the general integrals of the following linear PDES:(1) 2p+ xzq = y²(i) (y+1)p+(x+1)q = z.S. Find the integral surface of the linear PDEnoitpo to lioxp - yg =zb awhich contains the circle x² + y² =1, z =1.44INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS6. Find the equation of the integral surface of the PDEo s bai sA 319MA2y(z-3)p+(2x-z)q = y(2x- 3)which contains the circle x +y² = 2x, z = 0,7. Find the general integral of the PDEai ai 309 noris aTmoitide2(x- y)p+(y-x-z)q = zwhich contains the circle x² + y² =1, z =1.8. Find the solution of the equationlgoo sh be A MA(6+)(301 novis T2=-(p² +q°)+(p=x)(q-y)which passes through the x-axis.9. Find the characteristics of the equatione ia(s.a Pg = xryand determine the integral surface which passes through the curve z = x, y=0.10. Determine the characteristics of the equation2 = p? -q?and find the integral surface which passes through the parabola 4z+x² = 0, y = 0.*11. Show that the PDESxp = yq and z(xp + yq) = 2.xytidaare compatible and hence find its solution.12. Show that the equationsmo a9 mop? +q? =1_and (p² +q*)x= pzare compatible and hence find its solution.13. Find the complete integral of the equationओ न(p² +q²)x = pzwhere p=dzləx, q=dzləy.14. Find the complete integrals of the equationsbai(i) px - 4q°x² +6x²z– 2=0(ii) 2(z+ xp+ yq) = yp².15. Find the complete integral of the equationof he lp+q = pq. 3o soste leuinbelt16. Find the complete integrals of the following equations:(i) z pq = p+9(i) p°q² +x?y² = x°q?? + y?).

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Find the integral surface (general solution) of the differential equation dz (x+y)z.