Differential Equations Answers

Find the integral surface of the partial differential equation:(x–y) y^2 p+(y–x)x^2 q=(x^2 +y^2)z through the curve xz=a^2, y=0

Find the integral curves of the following equations:dx/(x^2–y^2–yz) = dy/(x^2–y^2–zx) = dz/[z(x–y)]

Apply the method of variations of parameters to solve the following differential equations: y" +a^2y=cosec ax

(x^2)d^2y/dx^2 –dy/dx –4x^3y =8x^3 sinx^2 ,x>0

Apply the method of variations of parameters to solve the following differential equations:x^2y" +xy'-y=x^2e^x

Solve the differential equation y''=1+(y')^2

To solve the initial value problem using the method of Laplace transforms:

y''+16y=8cos4t; y(0)=0; y'(0)=8

(y^2 +yz+ z^2)dx +(z^2 +zx+ x^2)dy + (x^2 +xy+ y^2)dz = 0

x^2p^²-2xyp+2y^2-x^2=0

Find the equation of the curve so drawn that every point on it is equidistant from the origin and the intersection of the x-axis with the normal to the curve at the point.