Solve the Differential equations

rocedwrp
2021-01-02
Answered

Solve the Differential equations

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asked 2022-01-21

Help to solve the following first order differential equations:

a.$x{y}^{4}dx+({y}^{2}+2){e}^{-5x}dy=0$

b.$(x+1){y}^{\prime}=x+6$

a.

b.

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 2022-09-11

How do you find the general solution of the differential equation $\frac{dy}{dx}=2{x}^{-3}$?

asked 2022-09-12

What is a general solution to the differential equation $1+{y}^{2}-y\prime \sqrt{1-{x}^{2}}=0$?

asked 2020-11-10

Find the sokaton 02 the ger Initial value provsem. $y\prime -y=8t2,y(0)=1$

asked 2022-09-11

What is a solution to the differential equation $\frac{dy}{dx}=\frac{y}{x}$?

asked 2022-05-21

My Problem is this given System of differential Equations:

$\dot{x}=8x+18y$

$\dot{y}=-3x-7y$

I am looking for a gerenal solution.

My Approach was: i can see this is a System of linear and ordinary differential equations. Both are of first-order, because the highest derivative is the first. But now i am stuck, i have no idea how to solve it. A Transformation into a Matrix should lead to this expression:

$\overrightarrow{y}=\left(\begin{array}{cc}8& 18\\ -3& -7\end{array}\right)\cdot x$

or is this correct:

$\overrightarrow{x}=\left(\begin{array}{cc}8& 18\\ -3& -7\end{array}\right)\cdot y\text{?}$

But i don't know how to determine the solution, from this point on.

$\dot{x}=8x+18y$

$\dot{y}=-3x-7y$

I am looking for a gerenal solution.

My Approach was: i can see this is a System of linear and ordinary differential equations. Both are of first-order, because the highest derivative is the first. But now i am stuck, i have no idea how to solve it. A Transformation into a Matrix should lead to this expression:

$\overrightarrow{y}=\left(\begin{array}{cc}8& 18\\ -3& -7\end{array}\right)\cdot x$

or is this correct:

$\overrightarrow{x}=\left(\begin{array}{cc}8& 18\\ -3& -7\end{array}\right)\cdot y\text{?}$

But i don't know how to determine the solution, from this point on.