Differential Equations Answers

Bernoulli’s Equation

(y^4 − 2xy)dx + 3x^2 dy = 0 when y(1)=0

Substitution as suggested by the equation

sinxsinydx + cosxcosydy = 0

Substitution as suggested by the equation

(x + 2y − 1)dx + 3(x + 2y)dy = 0 when y(0) = 2

Integrating factors found by inspection

y(x^2 y^2 − 1)dx + x(x^2 y^2 + 1)dy = 0

Integrating factors found by inspection

y(x^2 + y^2 − 1)dx + x(x^2 + y^2 + 1)dy = 0 when y(1) = 0

Use method of undetermined coefficients method to solve the following

y''+y=5xsinx,y(0)=0,y'(0)=1

Form the PDE of the following by eliminating arbitrary functions

phi(z^2-xy,x/z)

Solve the PDE whose auxiliary equations as follows: 𝑑𝑥/ 2𝑦(𝑧 − 3) = 𝑑𝑦 /𝑦(2𝑥 − 𝑧) = 𝑑𝑧 /𝑦(2𝑥 − 3)

dy/dx= y(xy^(5) − 1)

2. Solve by variation of parameters:

(D ^ 2 - 2D + 1) * y = x ^ (3/2) * e ^ x