15.18.27 problem 27

Internal problem ID [3270]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 27
Date solved : Monday, January 27, 2025 at 07:29:55 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }&={y^{\prime }}^{3} \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 37

dsolve(diff(y(x),x$2)+diff(y(x),x)=diff(y(x),x)^3,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\operatorname {arctanh}\left (\sqrt {-c_{1} {\mathrm e}^{2 x}+1}\right )+c_{2} \\ y \left (x \right ) &= \operatorname {arctanh}\left (\sqrt {-c_{1} {\mathrm e}^{2 x}+1}\right )+c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 60.114 (sec). Leaf size: 47

DSolve[D[y[x],{x,2}]+D[y[x],x]==D[y[x],x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_2-\text {arctanh}\left (\sqrt {1+e^{2 (x+c_1)}}\right ) \\ y(x)\to \text {arctanh}\left (\sqrt {1+e^{2 (x+c_1)}}\right )+c_2 \\ \end{align*}