Internal problem ID [10923]
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(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime \prime }-x {y^{\prime }}^{2} \sin \left (y\right )+2 \left (\cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }-\sin \left (x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve((x*cos(y(x))+sin(x))*diff(y(x),x$2)- x*diff(y(x),x)^2*sin(y(x)) + 2*(cos(y(x))+cos(x))*diff(y(x),x)=y(x)*sin(x),y(x), singsol=all)
\[ -y \left (x \right ) \sin \left (x \right )-x \sin \left (y \left (x \right )\right )-c_{1} x +c_{2} = 0 \]
✓ Solution by Mathematica
Time used: 0.187 (sec). Leaf size: 25
DSolve[(x*Cos[y[x]]+Sin[x])*y''[x]- x*y'[x]^2*Sin[y[x]] + 2*(Cos[y[x]]+Cos[x])*y'[x]==y[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\sin (y(x))+\frac {y(x) \sin (x)}{x}-\frac {c_1}{x}=c_2,y(x)\right ] \]