77.1.119 problem 146 (page 213)

Internal problem ID [18009]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 146 (page 213)
Date solved : Tuesday, January 28, 2025 at 11:19:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

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

\[ y = \csc \left (x \right ) \left (c_{1} +c_{2} +\left (c_{1} -c_{2} \right ) \cos \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 25

DSolve[Sin[x]^2*D[y[x],{x,2}]+Sin[x]*Cos[x]*D[y[x],x]==y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1-i c_2 \cos (x)}{\sqrt {\sin ^2(x)}} \]