75.6.7 problem 131

Internal problem ID [16763]
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 : 131
Date solved : Tuesday, January 28, 2025 at 09:21:36 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }-y \tan \left (x \right )&=\frac {1}{\cos \left (x \right )^{3}} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 9

dsolve([diff(y(x),x)-y(x)*tan(x)=1/cos(x)^3,y(0) = 0],y(x), singsol=all)
 

\[ y = \tan \left (x \right ) \sec \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 10

DSolve[{D[y[x],x]-y[x]*Tan[x]==1/Cos[x]^3,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \tan (x) \sec (x) \]