69.1.79 problem 124

Internal problem ID [14232]
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
Date solved : Tuesday, January 28, 2025 at 06:22:47 AM
CAS classification : [[_2nd_order, _missing_y]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.066 (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)
 

\[ y = -x -1+2 \sin \left (x \right )-\frac {\sin \left (2 x \right )}{2} \]

✓ Solution by Mathematica

Time used: 43.518 (sec). Leaf size: 87

DSolve[{D[y[x],{x,2}]+Tan[x]*D[y[x],x]==Sin[2*x],{y[0]==-1,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\cos (K[2]) \left (\int _1^{K[2]}2 \sin (K[1])dK[1]-\int _1^02 \sin (K[1])dK[1]\right )dK[2]-\int _1^0\cos (K[2]) \left (\int _1^{K[2]}2 \sin (K[1])dK[1]-\int _1^02 \sin (K[1])dK[1]\right )dK[2]-1 \]