Differential Equations Answers

Verify that the given differential equation is an exact: 

(3x²+2y)dx+(x-4y)dy=0

 Solve the first order linear inhomogeneous differential equation using the Bernoulli method

y^,-(2y/x)=1+(1/x)

Solve the first order linear inhomogeneous differential equation using the constant variation method

y^,- (3y/x)=x

F. Find the integral surface of the linear partial differential equation x(x^2+z)p - y(y^2+z)q = (x^2-y^2)z; p, q has their usual meaning , which contains the straight line. [CO1] *

I.In each of Problems 23 through 30, use the method of reduction of order to find a second solution of the given differential equation.

1.  t^2y″ − 4ty′ + 6y = 0, y1(t) = t^2

2.  xy″ − y′ + 4x^3y = 0, x > 0; y_1(x) = sin x^2

IV. Find the general solution of the given differential equation.

11/234) y‴ − y″ − y′ + y = 0

14/234) y^(4) − 4y‴ + 4y″ = 0

I.In each of Problems 23 through 30, use the method of reduction of order to find a second solution of the given differential equation.

1.  t2y″ − 4ty′ + 6y = 0, y1(t) = t2

2.  xy″ − y′ + 4x3y = 0, x > 0; y1(x) = sin x2

A spring is such that a 16 lb weight stretches it by 1.5 in. The weight is pulled down to a point

4 in below the equilibrium point and given an initial downward velocity of 4 ft/sec. An impressed

force of F(t) = 2 cos 74t is acting on the spring. Describe the motion.