Internal problem ID [13021]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-y=4 \cos \left (t^{2}\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 68
dsolve(diff(y(t),t)=y(t)+4*cos(t^2),y(t), singsol=all)
\[ y \left (t \right ) = \left (\frac {1}{4}-\frac {i}{4}\right ) \sqrt {2}\, {\mathrm e}^{t} \left (2 \,{\mathrm e}^{-\frac {i}{4}} \operatorname {erf}\left (\frac {\left (1-i+\left (2+2 i\right ) t \right ) \sqrt {2}}{4}\right ) \sqrt {\pi }+2 i \sqrt {\pi }\, {\mathrm e}^{\frac {i}{4}} \operatorname {erf}\left (\left (\frac {1}{4}-\frac {i}{4}\right ) \sqrt {2}\, \left (2 t +i\right )\right )+\left (1+i\right ) \sqrt {2}\, c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.137 (sec). Leaf size: 77
DSolve[y'[t]==y[t]+4*Cos[t^2],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^t \left (c_1-\sqrt [4]{-1} e^{-\frac {i}{4}} \sqrt {\pi } \left (\text {erfi}\left (\frac {1}{2} (-1)^{3/4} (2 t-i)\right )+i e^{\frac {i}{2}} \text {erfi}\left (\frac {1}{2} \sqrt [4]{-1} (2 t+i)\right )\right )\right ) \]