Differential Equations Answers

Verify that the given functions form the fundamental set of solution of the

differential equation on the given indicated interval.

y"-2y' + 5y = 0

y= c₁e^x cos 2x + c2₂e^x sin 2x, (-infinity, +infinity)

Use the method of variation of parameters to solve the system

𝑋′ =[

3 −1 −1

−2 3 2

4 −1 −2

]𝑋+[

1

𝑒𝑡

𝑒𝑡]

The differential equation (DE) of y'' + (5^3 + sinx)^5 y' + y = cosx^3 is?

Express 2/y²-1 in partial fractions. Hence solve the differential equation 2xdy/dx +1 = y² given that y= -3 when x= 1, expressing y explicitly in terms of x.

What is the value of y(π

2

)

y(π2) where y

′′

−2y

′

+y=xe

x

sinx

y″−2y′+y=xexsin⁡x ; y(0)=0

y(0)=0 and y

′

(0)=1

y′(0)=1 ?

The integral curves of "\\frac {dx}{a} = \\frac {dy}{b} = dz" is

The integral curves of dx/a = dy/b = dz is

((x^2) + 2)y′′ + xy' − 3y = 0

Solve the differential equation of the following homogeneous equation.

xydx + (x^2 + y^2)dy = 0