Differential Equations Answers

Verify that the differential equation (y^2+yz)dx+(xz+z^2)dy+(y^2-xy)dz=0 is integrable and find its primitive

9y''-4y=sinx

(3x+y-4)dx+(x+y-2)dy=0

solve power series solution

y'' - (x+1) y' -y = 0

solve power series solution

y'' - 2xy' + y = 0

Solve;  (𝑧 2 − 2𝑦𝑧 − 𝑦 2 )𝑝 + (𝑥𝑦 + 𝑧𝑥)𝑞 = 𝑥𝑦 − 𝑧x

Form the PDE by eliminating the arbitrary function from 𝑓 ( 𝑥−𝑦 𝑦−𝑧 , 𝑥𝑦 + 𝑦𝑧 + 𝑧𝑥) = 0.

Use Laplace transform to solve the differential equationy

′′−2y′−3y=0y″−2y′−3y=0

with the initial conditions y(0)=2y(0)=2 and y′(0)=−1y′(0)=−1 and y is a function of time t.

(D²-D')z=e^x-ysin(x+2y)

(D²-3DD'+2D'²)=e^2x-y+e^x+y