Question

Solve for the general solution

x^4y''''+4x^3y'''+3x^2y''-xy'+y=0

Answer #1

solve for x(t) and y(t):
x'=-3x+2y;
y'=-3x+4y
x(0)=0,y(0)=2

Use the elimination method to find a general solution for the
linear system: x'=3x-4y y'=4x-7y

find y' for the function
1. (y-2)^7=3x^2+2x-2
2. 3y^3+2x^3=3
3.(4y^2+3)^4+3x^5-5=0
4. 4x^2+3x^2y^2-y^3=3x

Solve the following:
(3x^2 - y^2)dx + (xy - x^3y^-1)dy = 0

Verify that the given function is the solution of the initial
value problem.
1. A) x^3y'''-3x^2y''+6xy'-6y= -(24/x) y(-1)=0 y'(-1)=0
y''(-1)=0
y=-6x-8x^2-3x^3+(1/x)
C) xy'''-y''-xy'+y^2= x^2 y(1)=2 y'(1)=5 y''(1)=-1
y=-x^2-2+2e^(x-1-e^-(x-1))+4x

Solve the given initial-value problem.
2y'' + 3y' −
2y = 10x2 −
4x − 15, y(0) = 0,
y'(0) = 0

(x+1)y'=y-1 2) dx+(x/y+(e)?)dy=0 3)ty'+2y=sint 4) y"-4y=-3x²e3x
5) y"-y-2y=1/sinx 6)2x2y"+xy'-2y=0 ea)y=x' b) x=0
2dx/dt-2dy/dt-3x=t; 2

1) Solve the system by elimination.
{8x−3y=−49
{4x-4y=-32
a) One solution:
b) No solution
c) Infinite number of solutions
2) Solve the system by elimination.
{5x+2y=−5
{3x-5y=28
a) One solution:
b) No solution
c) Infinite number of solutions

Find the general solution. Express the solution in vector
form.
x' = x + 2y
y' = 4x+3y
Find the general solution. Express the solution in scalar
form.
x' = −4x + 2y
y' = − 5/2 x + 2y

Find the general solution near x = 0 of y'' - xy' + 2y = 0.
(Power series, recursive formula problem)

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