Question

Find the differential Equation of

xy'-2y+(2x^3)e^-x=0

Answer #1

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Differential Equations
Use principle of superposition to find a particular solution
x^2y''- xy+y =2x^3

Find the solution of the Differential Equation
X^2y''-xy'+y=x

Find the particular integral of the differential equation
d2y/dx2 + 3dy/dx + 2y = e −2x
(x + 1). show that the answer is yp(x) = −e −2x ( 1/2
x2 + 2x + 2)

Consider the following differential equation 32x 2y
'' + 3 (1 − e 2x )y = 0 (b) Determine the indicial
equation and find its roots. (c) Without solving the problem,
formally write the two linearly independent solutions near x = 0.
(d) What can you say about the radius of convergence of the power
series in (c)? (e) Find the first three non-zero terms of the two
linearly independent solutions.

Verify that the function
y=x^2+c/x^2
is a solution of the differential equation
xy′+2y=4x^2, (x>0).
b) Find the value of c for which the solution satisfies the initial
condition y(4)=3.
c=

differential equation one solution is given,
xy''-(2x+1)y'+(x+1)y=x^2; y_1=e^x

Differential Equations problem
If y1= e^-x is a solution of the differential equation
y'''-y''+2y=0 . What is the general solution of the differential
equation?

solve differential equation
(x^2)y'' - xy' +y =2x

solve the given differential equation by undetermined
coefficients. y"-y'-2y=e^2x

3. Find the equation of the tangent line to the curve 2x^3 + y^2
= xy at the point (−1, 1).
4. Use implicit differentiation to find y' for sin(xy^2 ) − x^3
= 4x + 2y.
5. Use logarithmic differentiation to find y' for y = e^4x
cos(2x) / (x−1)^4 .
6. Show that d/dx (tan (x)) = sec^2 (x) using only your
knowledge of the derivatives of sine/cosine with derivative
rules.
7. Use implicit differentiation to show that...

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