Internal problem ID [10922]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page
221
Problem number: Problem 19(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {\frac {x y^{\prime \prime }}{y+1}+\frac {y^{\prime } y-x {y^{\prime }}^{2}+y^{\prime }}{\left (y+1\right )^{2}}-\sin \left (x \right ) x=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 27
dsolve(x*diff(y(x),x$2)/(1+y(x))+( y(x)*diff(y(x),x)-x* diff(y(x),x)^2+diff(y(x),x))/( 1+y(x))^2=x*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {\pi \,\operatorname {csgn}\left (x \right )}{2}} x^{-c_{2}} {\mathrm e}^{-\sin \left (x \right )} {\mathrm e}^{\operatorname {Si}\left (x \right )} c_{1} -1 \]
✓ Solution by Mathematica
Time used: 0.438 (sec). Leaf size: 23
DSolve[x*y''[x]/(1+y[x])+( y[x]*y'[x]-x* y'[x]^2+y'[x])/( 1+y[x])^2==x*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1+x^{c_2} e^{\text {Si}(x)-\sin (x)+c_1} \\ \end{align*}