73.1.20 problem 2.3 (j)

Internal problem ID [14998]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.3 (j)
Date solved : Tuesday, January 28, 2025 at 07:27:14 AM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(diff(y(x),x$2)=sin(2*x),y(x), singsol=all)
 

\[ y = -\frac {\sin \left (2 x \right )}{4}+c_{1} x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 32

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

\[ y(x)\to \int _1^x\int _1^{K[2]}\sin (2 K[1])dK[1]dK[2]+c_2 x+c_1 \]