Internal problem ID [13373]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+6 y x=\sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 77
dsolve([diff(y(x),x)+6*x*y(x)=sin(x),y(0) = 4],y(x), singsol=all)
\[ y \left (x \right ) = 4 \,{\mathrm e}^{-3 x^{2}}-\frac {\sqrt {3}\, \sqrt {\pi }\, {\mathrm e}^{-3 x^{2}+\frac {1}{12}} \operatorname {erf}\left (\frac {\sqrt {3}}{6}\right )}{6}+\frac {\sqrt {3}\, \sqrt {\pi }\, {\mathrm e}^{-3 x^{2}+\frac {1}{12}} \operatorname {erf}\left (\frac {\sqrt {3}\, \left (6 i x +1\right )}{6}\right )}{12}-\frac {\sqrt {3}\, \sqrt {\pi }\, {\mathrm e}^{-3 x^{2}+\frac {1}{12}} \operatorname {erf}\left (\frac {\sqrt {3}\, \left (6 i x -1\right )}{6}\right )}{12} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 105
DSolve[{y'[x]+6*x*y[x]==Sin[x],{y[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{12} e^{-3 x^2} \left (\sqrt [12]{e} \sqrt {3 \pi } \text {erf}\left (\frac {1+6 i x}{2 \sqrt {3}}\right )-2 \sqrt [12]{e} \sqrt {3 \pi } \text {erf}\left (\frac {1}{2 \sqrt {3}}\right )-i \sqrt [12]{e} \sqrt {3 \pi } \text {erfi}\left (\frac {6 x+i}{2 \sqrt {3}}\right )+48\right ) \]