Internal problem ID [2701]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 54.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _Riccati]
\[ \boxed {y^{\prime }-\left (9 x -y\right )^{2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.157 (sec). Leaf size: 28
dsolve([diff(y(x),x)=(9*x-y(x))^2,y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (9 x -3\right ) {\mathrm e}^{6 x}+9 x +3}{1+{\mathrm e}^{6 x}} \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 31
DSolve[{y'[x]==(9*x-y[x])^2,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {9 x+e^{6 x} (9 x-3)+3}{e^{6 x}+1} \]