kramtus51
2022-01-19
Answered

Solve for G.S./P.S. for the following differential equations using the solutions by a change in variables as suggested by the equations.

$({t}^{2}{e}^{t}-4{x}^{2})dt+8txdx=0$

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einfachmoipf

Answered 2022-01-19
Author has **32** answers

Integrating

asked 2020-11-27

Solve differential equation
$x\frac{dy}{dx}-2y={x}^{3}{\mathrm{sin}}^{2}\left(x\right)$

asked 2021-03-05

Solve differential equation
$dy/dx-12{x}^{3}y={x}^{3}$

asked 2022-01-19

Dont

asked 2022-01-21

Are the following are linear equation?

$1.\text{}\frac{dP}{dt}+2tP=P+4t-2$

$2.\text{}\frac{dy}{dx}={y}^{2}-3y$

asked 2022-01-22

Solve the equation separable, linear, bernoulli, or homogenous

$1.\frac{dy}{dx}=\frac{{x}^{4}+4x{y}^{2}}{2{x}^{3}+{x}^{2}y+{y}^{3}}$

$2.\left({e}^{-y}\mathrm{cos}\left(x\right)\right){y}^{\prime}={x}^{4}+6{x}^{2}{y}^{3}$

$3.{y}^{\prime}=\frac{y+y{x}^{3}}{x+{x}^{2}}\mathrm{cos}\left(\frac{{x}^{2}}{{y}^{2}}\right)$

asked 2022-01-21

Write an equivalent first-order differential equation and initial condition for y.

What is the equivalent first-order differential equation?

What is the initial condition?

asked 2022-04-12

What method would you use to solve:

$(1+{x}^{2})\frac{\mathrm{d}y}{\mathrm{d}x}=1+{y}^{2}\phantom{\rule{thickmathspace}{0ex}};\phantom{\rule{2em}{0ex}}y(2)=3$

I am asking this because I only know two methods of solving the DEs - separation of variables and integrating factor. Since the separation of variables does not work here, I tried integrating factor, however, I don't know what to do with the y2, because for the IF to work I need to get y on its own $\frac{\mathrm{d}y}{\mathrm{d}x}+P(x)y=Q(x)$)

What method do I use to solve this?

$(1+{x}^{2})\frac{\mathrm{d}y}{\mathrm{d}x}=1+{y}^{2}\phantom{\rule{thickmathspace}{0ex}};\phantom{\rule{2em}{0ex}}y(2)=3$

I am asking this because I only know two methods of solving the DEs - separation of variables and integrating factor. Since the separation of variables does not work here, I tried integrating factor, however, I don't know what to do with the y2, because for the IF to work I need to get y on its own $\frac{\mathrm{d}y}{\mathrm{d}x}+P(x)y=Q(x)$)

What method do I use to solve this?