57.1.60 problem 60

Internal problem ID [9044]
Book : First order enumerated odes
Section : section 1
Problem number : 60
Date solved : Monday, January 27, 2025 at 05:27:57 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\sqrt {1+6 x +y} \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 57

dsolve(diff(y(x),x)=(1+6*x+y(x))^(1/2),y(x), singsol=all)
 

\[ x -2 \sqrt {1+6 x +y}+6 \ln \left (6+\sqrt {1+6 x +y}\right )-6 \ln \left (-6+\sqrt {1+6 x +y}\right )+6 \ln \left (-35+6 x +y\right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 11.355 (sec). Leaf size: 112

DSolve[D[y[x],x]==(1+6*x+y[x])^(1/2),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 36 W\left (-\frac {1}{6} e^{\frac {1}{72} (-6 x-73+6 c_1)}\right ){}^2+72 W\left (-\frac {1}{6} e^{\frac {1}{72} (-6 x-73+6 c_1)}\right )-6 x+35 \\ y(x)\to 35-6 x \\ y(x)\to 36 W\left (-\frac {1}{6} e^{\frac {1}{72} (-6 x-73)}\right )^2+72 W\left (-\frac {1}{6} e^{\frac {1}{72} (-6 x-73)}\right )-6 x+35 \\ \end{align*}