Internal problem ID [1705]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.10. Page 80
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{\left (-t +y\right )^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 24
dsolve(diff(y(t),t)= exp((y(t)-t)^2),y(t), singsol=all)
\[ y \relax (t ) = t +\RootOf \left (-t +\int _{}^{\textit {\_Z}}\frac {1}{-1+{\mathrm e}^{\textit {\_a}^{2}}}d \textit {\_a} +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.678 (sec). Leaf size: 241
DSolve[y'[t]== Exp[(y[t]-t)^2],y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^t-\frac {e^{(y(t)-K[1])^2}}{-1+e^{(y(t)-K[1])^2}}dK[1]+\int _1^{y(t)}-\frac {e^{(t-K[2])^2} \int _1^t\left (\frac {2 e^{2 (K[2]-K[1])^2} (K[2]-K[1])}{\left (-1+e^{(K[2]-K[1])^2}\right )^2}-\frac {2 e^{(K[2]-K[1])^2} (K[2]-K[1])}{-1+e^{(K[2]-K[1])^2}}\right )dK[1]-\int _1^t\left (\frac {2 e^{2 (K[2]-K[1])^2} (K[2]-K[1])}{\left (-1+e^{(K[2]-K[1])^2}\right )^2}-\frac {2 e^{(K[2]-K[1])^2} (K[2]-K[1])}{-1+e^{(K[2]-K[1])^2}}\right )dK[1]-1}{-1+e^{(t-K[2])^2}}dK[2]=c_1,y(t)\right ] \]