61.2.53 problem Problem 19(f)

Internal problem ID [15291]
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 : Thursday, October 02, 2025 at 10:11:13 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*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 20

ode:=(cos(y(x))-y(x)*sin(y(x)))*diff(diff(y(x),x),x)-diff(y(x),x)^2*(2*sin(y(x))+y(x)*cos(y(x))) = sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ -y \cos \left (y\right )-c_1 x -\sin \left (x \right )+c_2 = 0 \]

✗ Mathematica

ode=(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]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-y(x)*sin(y(x)) + cos(y(x)))*Derivative(y(x), (x, 2)) - (y(x)*cos(y(x)) + 2*sin(y(x)))*Derivative(y(x), x)**2 - sin(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out