Internal problem ID [10926]
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(f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {\left (\cos \left (y\right )-y \sin \left (y\right )\right ) y^{\prime \prime }-{y^{\prime }}^{2} \left (2 \sin \left (y\right )+y \cos \left (y\right )\right )-\sin \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve((cos(y(x))-y(x)*sin(y(x)))*diff(y(x),x$2)- diff(y(x),x)^2* (2*sin(y(x))+y(x)*cos(y(x))) =sin(x),y(x), singsol=all)
\[ -y \left (x \right ) \cos \left (y \left (x \right )\right )-c_{1} x -\sin \left (x \right )+c_{2} = 0 \]
✓ Solution by Mathematica
Time used: 0.337 (sec). Leaf size: 28
DSolve[(Cos[y[x]]-y[x]*Sin[y[x]])*y''[x]- y'[x]^2* (2*Sin[y[x]]+y[x]*Cos[y[x]])==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x) \cos (y(x))}{x}+\frac {\sin (x)}{x}+\frac {c_1}{x}=c_2,y(x)\right ] \]