75.4.34 problem 99

Internal problem ID [16736]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 99
Date solved : Tuesday, January 28, 2025 at 08:26:00 PM
CAS classification : [_separable]

\begin{align*} x^{2} y^{\prime }+\sin \left (2 y\right )&=1 \end{align*}

With initial conditions

\begin{align*} y \left (\infty \right )&=\frac {11 \pi }{4} \end{align*}

✓ Solution by Maple

Time used: 0.641 (sec). Leaf size: 20

dsolve([x^2*diff(y(x),x)+sin(2*y(x))=1,y(infinity) = 11/4*Pi],y(x), singsol=all)
 

\[ y = -\arctan \left (\frac {x +2}{x -2}\right )+3 \pi \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{x^2*D[y[x],x]+Sin[2*y[x]]==1,{y[Infinity]==11/4*Pi}},y[x],x,IncludeSingularSolutions -> True]
 

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