Internal problem ID [15033]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\tan \left (x \right ) y=\frac {1}{\cos \left (x \right )^{3}}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve([diff(y(x),x)-y(x)*tan(x)=1/cos(x)^3,y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \sec \left (x \right ) \tan \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 10
DSolve[{y'[x]-y[x]*Tan[x]==1/Cos[x]^3,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \tan (x) \sec (x) \]