67.2.53 problem Problem 19(f)

Internal problem ID [14010]
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)
Date solved : Tuesday, January 28, 2025 at 06:12:30 AM
CAS classification : [[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} \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 ) \end{align*}

✓ Solution by Maple

Time used: 0.219 (sec). Leaf size: 17

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)
 

\[ y \cos \left (y\right )-c_{1} x +\sin \left (x \right )+c_{2} = 0 \]

✓ Solution by Mathematica

Time used: 0.270 (sec). Leaf size: 28

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

\[ \text {Solve}\left [\frac {y(x) \cos (y(x))}{x}+\frac {\sin (x)}{x}+\frac {c_1}{x}=c_2,y(x)\right ] \]