How to solve this equation

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2020-11-08
Answered

How to solve this equation

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Pohanginah

Answered 2020-11-09
Author has **96** answers

Solve:

The equation is

Variation of Parameters:

The homogeneous equation is

The homogeneous solution is

Obtain the Wro

ians:

The values of

Further we have

asked 2020-11-09

Solve for the general solution of the given special second-ordered differential equation

$x{y}^{\u2033}+x({y}^{\prime}{)}^{2}-{y}^{\prime}=0$

asked 2021-03-08

Solve differential equation ${y}^{\prime}+y=x,\text{}y\left(0\right)=1$

asked 2022-01-17

Help with a generating function and differential equation

I have a generating function that Im

I have a generating function that Im

asked 2022-07-02

I have the following differential equation

$s(1-s)t={f}^{\prime}(t)(f(t)-st)$

Initial condition: $f(0)=0.$

I solved it and got the solution as

$f(t)=\sqrt{2{c}_{1}+{s}^{2}-2(s-1)s\mathrm{ln}(t)}+s$

But the answer given is

$f(t)=k(s)t,$

where

$k(s)=\frac{s+\sqrt{4s-3{s}^{2}}}{2}.$

If anyone can provide me some hint on how to proceed and reach the specified answer, I would be really grateful.

$s(1-s)t={f}^{\prime}(t)(f(t)-st)$

Initial condition: $f(0)=0.$

I solved it and got the solution as

$f(t)=\sqrt{2{c}_{1}+{s}^{2}-2(s-1)s\mathrm{ln}(t)}+s$

But the answer given is

$f(t)=k(s)t,$

where

$k(s)=\frac{s+\sqrt{4s-3{s}^{2}}}{2}.$

If anyone can provide me some hint on how to proceed and reach the specified answer, I would be really grateful.

asked 2022-06-01

I have been having a problem with this simple equation. It is asking me this: Find all values of $k$ for which the function $y=\mathrm{sin}(kt)$ satisfies the differential equation $y\prime \prime +7y=0$.

I have found the second derivative, plugged it back into the differential equation, and found out $\sqrt{7}$ checked, but $-\sqrt{7}$ did not. Please help me solve this question.

I have found the second derivative, plugged it back into the differential equation, and found out $\sqrt{7}$ checked, but $-\sqrt{7}$ did not. Please help me solve this question.

asked 2022-06-19

The equation is:

${e}^{x}(1+x)dx=(x{e}^{x}-y{e}^{y})dy$

I've tried solving this as a non-exact differential equation but it's definitely incorrect. Not sure if this can be classified as an Bernoulli/Linear Differential equation either.

Any help is appreciated!

${e}^{x}(1+x)dx=(x{e}^{x}-y{e}^{y})dy$

I've tried solving this as a non-exact differential equation but it's definitely incorrect. Not sure if this can be classified as an Bernoulli/Linear Differential equation either.

Any help is appreciated!

asked 2022-04-14

Laplace transform of $f\left(t\right)=t{e}^{-t}\mathrm{sin}\left(2t\right)$