71.4.16 problem 16

Internal problem ID [14388]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 06:29:19 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (2\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.045 (sec). Leaf size: 23

dsolve([diff(y(x),x)=x^2+exp(x)-sin(x),y(2) = -1],y(x), singsol=all)
 

\[ y = \frac {x^{3}}{3}+\cos \left (x \right )+{\mathrm e}^{x}-\frac {11}{3}-\cos \left (2\right )-{\mathrm e}^{2} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 28

DSolve[{D[y[x],x]==x^2+Exp[x]-Sin[x],{y[2]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _2^x\left (K[1]^2+e^{K[1]}-\sin (K[1])\right )dK[1]-1 \]