Internal problem ID [12701]
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: 57
dsolve(diff(y(t),t)=y(t)+4*cos(t^2),y(t), singsol=all)
\[ y \left (t \right ) = \left (\frac {\sqrt {\pi }\, {\mathrm e}^{\frac {i}{4}} \operatorname {erf}\left (\sqrt {-i}\, t +\frac {1}{2 \sqrt {-i}}\right )}{\sqrt {-i}}-\sqrt {\pi }\, {\mathrm e}^{-\frac {i}{4}} \left (-1\right )^{\frac {3}{4}} \operatorname {erf}\left (\left (-1\right )^{\frac {1}{4}} t -\frac {\left (-1\right )^{\frac {3}{4}}}{2}\right )+c_{1} \right ) {\mathrm e}^{t} \]
✓ 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]
\[ y(t)\to e^t \left (c_1-\sqrt [4]{-1} e^{-\frac {i}{4}} \sqrt {\pi } \left (\text {erfi}\left (\frac {1}{2} (-1)^{3/4} (2 t-i)\right )+i e^{\frac {i}{2}} \text {erfi}\left (\frac {1}{2} \sqrt [4]{-1} (2 t+i)\right )\right )\right ) \]