73.4.27 problem 5.4 (a)

Internal problem ID [15109]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.4 (a)
Date solved : Tuesday, January 28, 2025 at 07:31:05 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+6 y x&=\sin \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.140 (sec). Leaf size: 89

dsolve([diff(y(x),x)+6*x*y(x)=sin(x),y(0) = 4],y(x), singsol=all)
 

\[ y = 4 \,{\mathrm e}^{-3 x^{2}}-\frac {\sqrt {3}\, \sqrt {\pi }\, {\mathrm e}^{-3 x^{2}+\frac {1}{12}} \operatorname {erf}\left (\frac {\sqrt {3}}{6}\right )}{6}-\frac {\sqrt {3}\, \sqrt {\pi }\, {\mathrm e}^{-3 x^{2}+\frac {1}{12}} \operatorname {erf}\left (\frac {\sqrt {3}\, \left (6 i x -1\right )}{6}\right )}{12}+\frac {\sqrt {3}\, \sqrt {\pi }\, {\mathrm e}^{-3 x^{2}+\frac {1}{12}} \operatorname {erf}\left (\frac {\sqrt {3}\, \left (6 i x +1\right )}{6}\right )}{12} \]

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 34

DSolve[{D[y[x],x]+6*x*y[x]==Sin[x],{y[0]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x^2} \left (\int _0^xe^{3 K[1]^2} \sin (K[1])dK[1]+4\right ) \]