Question

3. Find the general solution to each of the following differential equations.

(a) y'' - 3y' + 2y = 0

(b) y'' - 10y' = 0

(c) y'' + y' - y = 0

(d) y'' + 2y' + y = 0

Answer #1

Find the general solution of the following differential
equations. Primes denote derivates with respect to x.
1) x(x+3y)y'= y(x-3y)
2) 3xy^2y'= 21x^3+3y^3
3) x^2y'= xy+10y^2
4) x(4x+3y)y'+ y(12x+3y)= 0
5)2xyy' = 2y^2 + 7xsqrt(9x^2+y^2)

Oridinary Differential equations:
given that y=sinx is a solution of
y(4)+2y'''+11y''+2y'+10y=0,
find the general solution of the DE.

Solve the following second order differential equations:
(a) Find the general solution of y'' − 2y' = sin(3x) using the
method of undetermined coefficients.
(b) Find the general solution of y'' − 2y'− 3y = te^−t using the
method of variation of parameters.

Find the general solution of the differential equation
y′′ − 2y′ − 3y = ae3t, where a is a constant

For each of the following equations, find the general solution
(perferably using imaginary numbers):
y′′ −2y′ −3y=3e2t;
y′′ +2y′ =3+sin(2t);
x2y′′ +7xy′ +5y=x;
x2y′′ +xy′ +4y=sin(lnx)+sin(2lnx);
y′′ +y=tcost.

Find the general solution of the differential equation:
y''' - 3y'' + 3y' - y = e^x - x + 16
y' being the first derivative of y(x), y'' being the second
derivative, etc.

4. For each of the following equations find the general
solution.
(a) y" + 2y' + 2y = etsin(t)
(b) y(4) - 4y" + 4y = et -
te2t

solve the following system of differential equations
and find the general solution
(D+3)x+(D-1)y=0 and 2x+(D-3)y=0
please show the steps

a) Find the general solution of the differential equation
y''-2y'+y=0
b) Use the method of variation of parameters to find the general
solution of the differential equation y''-2y'+y=2e^t/t^3

Find the general solution of the following nonhomogeneous
equations:
• y '' − 2y ' + 5y = 25x ^2 + 12
• y ''− 3y ' + 2y = 10 sen 2x
• y '' − 2y ' + y = e^x + e^−2x
• y '' − y = x sen x
• y '' − 6y ' + 9y = 5e^x sen x
• y '' + y ' + y + 1 = sen x +...

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