Differential Equations Answers

When do we identify an equation as homogeneous?

y^''-x²y'-2xy=0;y(0)=1&y'(0)=0 solve by reduction of order

2) Solve the following system

𝑑𝑥

𝑑𝑡

= 𝑥 + 𝑦

𝑑𝑦

𝑑𝑡

= −2𝑥 − 𝑦 

1) Find the half range Fourier cosine and sine series for

𝑓(𝑤) = 1 − 𝑤; 0 < 𝑤 < 1

Reduce the equation Zxx - (1+y)² Zyy = 0 to canonical form

(D+3)^2y=sinh2x

Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. Form the general solution x^3 (y''') + 6x^2 (y'') + 4xy' - 4y =0; x, x^-2, x^-2 (lnx), (0,infinity)?

Solve yzdx-xzdy-(x^2+y^2)tan^-1(y/x)dz=0

Using power series method to solve the initial value problem

(x − )1 y′′ + yx ′ + y = 0 , y )0( = 2 , y′ )0( = −1 .

1.Solve Cos y cos px + sin y sin px = p

2.Solve

(D^3+2D^2+D)y= e^2x + x^2 + sin2x