Solve the differential equation.

$5\sqrt{xy}\frac{dy}{dx}=1,x,y>0$

Cem Hayes
2021-09-18
Answered

Solve the differential equation.

$5\sqrt{xy}\frac{dy}{dx}=1,x,y>0$

You can still ask an expert for help

StrycharzT

Answered 2021-09-19
Author has **102** answers

Step 1

Given,

$5\sqrt{xy}\frac{dy}{dx}=1,x,y>0$

Step 2

Rewriting the equation,

$5\sqrt{y}dy=\frac{1}{\sqrt{x}}dx$

Step 3

Integrate both sides,

$\Rightarrow 5\int \sqrt{y}dy=\int \frac{1}{\sqrt{x}}dx+C$ , C is constant.

$\Rightarrow 5\left(\frac{{y}^{\frac{1}{2}+1}}{\frac{1}{2}+1}\right)=\left(\frac{{x}^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}\right)+C$

$\Rightarrow 5\left(\frac{2{y}^{\frac{3}{2}}}{3}\right)=2{x}^{\frac{1}{2}}+C$

$\Rightarrow {y}^{\frac{3}{2}}=\frac{3}{10}(2{x}^{\frac{1}{2}}+C)$

$\Rightarrow y={\left(\frac{3}{10}\left(2{x}^{\frac{1}{2}+C}\right)\right)}^{\frac{2}{3}}$

Given,

Step 2

Rewriting the equation,

Step 3

Integrate both sides,

asked 2020-10-18

Find a least squares solution of Ax=b by constructing and solving the normal equations.

$A=\left[\begin{array}{cc}3& 1\\ 1& 1\\ 1& 4\end{array}\right],b\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]$

$\stackrel{\u2015}{x}=$ ?

asked 2021-10-01

Solve quadratic equation.

$9-6x+{x}^{2}=0$

asked 2021-11-21

Solve the rational equation.

$\frac{7}{x}+x=\frac{88}{x}$

asked 2021-09-18

Use the discriminant to determine whether each quadratic equation has two unequal real solutions, a repeated real solution (a double root), or no real solution, without solving the equation.

$3{x}^{2}+5x-8=0$

asked 2021-02-26

Use the Cauchy-Riemann equations to show that $f\left(z\right)=\stackrel{\u2015}{z}$ is not analytic.

asked 2021-09-15

Determine if the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify. (2x + 1)/3 + (x - 4)/6

asked 2022-05-07

Solve for x in the equation 1-4x=0.