60.1.197 problem 198

Internal problem ID [10211]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 198
Date solved : Monday, January 27, 2025 at 06:38:47 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

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

\[ y = -\sin \left (x \right )+\tan \left (x \right ) c_{1} \]

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 21

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

\[ y(x)\to \tan (x) \left (\int _1^x\sin (K[1])dK[1]+c_1\right ) \]