75.6.5 problem 129

Internal problem ID [16761]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 129
Date solved : Tuesday, January 28, 2025 at 09:21:31 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 10

dsolve([diff(y(x),x)*cos(x)-y(x)*sin(x)=2*x,y(0) = 0],y(x), singsol=all)
 

\[ y = \sec \left (x \right ) x^{2} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 11

DSolve[{D[y[x],x]*Cos[x]-y[x]*Sin[x]==2*x,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 \sec (x) \]