Internal problem ID [11393]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises
page 26
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _Riccati]
\[ \boxed {x^{\prime }-\left (4 t -x\right )^{2}=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 28
dsolve([diff(x(t),t)=(4*t-x(t))^2,x(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = \frac {\left (4 t -2\right ) {\mathrm e}^{4 t}+12 t +6}{3+{\mathrm e}^{4 t}} \]
✓ Solution by Mathematica
Time used: 0.271 (sec). Leaf size: 31
DSolve[{x'[t]==(4*t-x[t])^2,{x[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {12 t+e^{4 t} (4 t-2)+6}{e^{4 t}+3} \]