Differential Equations Answers

1. Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation

x dy/dx - (1+x)y = x(y)^2


2. Solve the given initial-value problem. The DE is a Bernoulli equation.

x^2 dy/dx - 2xy = 4y^4, y(1)= 1/2

A mass of 250 g stretches a spring 1.568 cm. If the mass is set in motion from its equilibrium position with a downward velocity of 20 cm/s, and if there is no damping, determine the position u of the mass at any time t.


Enclose arguments of functions in parentheses. For example, sin(2x).
Assume g = 9.8 m/s^2. Enter an exact answer.

u(t) = _____ m

Use the method of variation of parameters to find a particular solution of the differential equation

y′′−2y′−15y=384e^−t.

Solve the initial value problem

y′′+4y′+4y=0, y(−1)=4, y′(−1)=4

Find a particular solution of the given differential equation. Use a CAS as an aid in carrying out differentiations, simplifications, and algebra.

y^(4) + 2y'' + y = 1 cos x − 3x sin x

Solve the given differential equation by undetermined coefficients.

y'' + y' + y = x sin x

Solve (x+2z)p+(4xz-y)q=x^2+y

Solve (2D^3+3D^2D'+4DD'^2+5D'^3)z=x^2+y

Regular singular point for differential equationx(x-2)²d²y/dx²+2(x-2)dy/dx+(x+3)y=0