4.37 problem Problem 54

Internal problem ID [2192]

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]

Solve \begin {gather*} \boxed {y^{\prime }-\left (9 x -y\right )^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}

Solution by Maple

Time used: 0.127 (sec). Leaf size: 28

dsolve([diff(y(x),x)=(9*x-y(x))^2,y(0) = 0],y(x), singsol=all)
 

\[ y \relax (x ) = \frac {\left (9 x -3\right ) {\mathrm e}^{6 x}+9 x +3}{1+{\mathrm e}^{6 x}} \]

Solution by Mathematica

Time used: 0.143 (sec). Leaf size: 15

DSolve[{y'[x]==(9*x-y[x])^2,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 9 x-3 \tanh (3 x) \\ \end{align*}