Calculus

First Order Differential Equations

Differential Equations - Variable Separable

         

What is the solution of the following differential equation: (dydx)5xdydx+y=0?\left(\frac{dy}{dx}\right)^{5}-x\frac{dy}{dx}+y=0?

Note: CC is a constant.

What is the solution of the differential equation 15(1x3dxdy1x2y)=ysiny2? \frac{1}{5}\left(\frac{1}{{x}^{3}}\frac{dx}{dy}-\frac{1}{{x}^{2}}y\right) =y\sin{{y}^{2}} ?

Details and assumptions

Use CC as the constant of integration.

What is the solution of the differential equation (8x25yx2)dydx+(5y3+xy3)=0,y(1)=1?\begin{aligned} (8x^2-5yx^2)\frac{dy}{dx}+(5y^3+xy^3) &=0, \\ y(1) &=1? \end{aligned}

What is the solution of the differential equation logdydx=8x+7y,y(0)=0?\begin{aligned} \log{\frac{dy}{dx}} &=8x+7y,\\ y(0)&=0? \end{aligned}

Note: In this problem, log(x)\log(x) is the natural logarithm (log base e) of x.x.

What is the solution of the differential equation logdydx=5x+2y,y(0)=0?\log{\frac{dy}{dx}}=5x+2y, y(0)=0?

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