Internal problem ID [12496]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 124.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+y^{\prime } \tan \left (x \right )=\sin \left (2 x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 19
dsolve([diff(y(x),x$2)+tan(x)*diff(y(x),x)=sin(2*x),y(0) = -1, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -x -1+2 \sin \left (x \right )-\frac {\sin \left (2 x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.154 (sec). Leaf size: 18
DSolve[{y''[x]+Tan[x]*y'[x]==Sin[2*x],{y[0]==-1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x-\sin (x) (\cos (x)-2)-1 \]