60.1.536 problem 539

Internal problem ID [10550]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 539
Date solved : Monday, January 27, 2025 at 08:54:39 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{3} \sin \left (x \right )-\left (y \sin \left (x \right )-\cos \left (x \right )^{2}\right ) {y^{\prime }}^{2}-\left (y \cos \left (x \right )^{2}+\sin \left (x \right )\right ) y^{\prime }+y \sin \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.059 (sec). Leaf size: 32

dsolve(diff(y(x),x)^3*sin(x)-(y(x)*sin(x)-cos(x)^2)*diff(y(x),x)^2-(y(x)*cos(x)^2+sin(x))*diff(y(x),x)+y(x)*sin(x)=0,y(x), singsol=all)
 

\begin{align*} y &= {\mathrm e}^{x} c_{1} \\ y &= -\ln \left (\csc \left (x \right )-\cot \left (x \right )\right )+c_{1} \\ y &= -\cos \left (x \right )+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 38

DSolve[Sin[x]*y[x] - (Sin[x] + Cos[x]^2*y[x])*D[y[x],x] - (-Cos[x]^2 + Sin[x]*y[x])*D[y[x],x]^2 + Sin[x]*D[y[x],x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^x \\ y(x)\to \text {arctanh}(\cos (x))+c_1 \\ y(x)\to \int _1^x\sin (K[1])dK[1]+c_1 \\ \end{align*}