83.48.13 problem Ex 13 page 108

Internal problem ID [19605]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VII. Exact differential equations.
Problem number : Ex 13 page 108
Date solved : Tuesday, January 28, 2025 at 02:03:58 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }+{y^{\prime }}^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 35

dsolve(diff(y(x),x$2)+diff(y(x),x)+diff(y(x),x)^3=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 60.070 (sec). Leaf size: 69

DSolve[D[y[x],{x,2}]+D[y[x],x]+D[y[x],x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

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