85.33.42 problem 42

Internal problem ID [22665]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 42
Date solved : Thursday, October 02, 2025 at 09:03:21 PM
CAS classification : [_exact]

\begin{align*} \left (\sin \left (y\right )-x \right ) y^{\prime }&=2 x +y \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=\frac {\pi }{2} \\ \end{align*}

✓ Maple. Time used: 0.045 (sec). Leaf size: 23

ode:=(sin(y(x))-x)*diff(y(x),x) = y(x)+2*x; 
ic:=[y(1) = 1/2*Pi]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (2 \textit {\_Z} x +2 x^{2}+2 \cos \left (\textit {\_Z} \right )-\pi -2\right ) \]

✓ Mathematica. Time used: 0.153 (sec). Leaf size: 22

ode=(Sin[y[x]]-x)*D[y[x],{x,1}]==2*x+y[x]; 
ic={y[1]==Pi/2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x^2+x y(x)+\cos (y(x))=\frac {2+\pi }{2},y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x + (-x + sin(y(x)))*Derivative(y(x), x) - y(x),0) 
ics = {y(1): pi/2} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(-2*x - y(x))/(x - sin(y(x))) + Derivative(y(x), x) cannot be s