58.2.7 problem 8

Internal problem ID [9130]
Book : Second order enumerated odes
Section : section 2
Problem number : 8
Date solved : Monday, January 27, 2025 at 05:45:55 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\left (x +y\right )^{4} \end{align*}

✓ Solution by Maple

Time used: 0.618 (sec). Leaf size: 882

dsolve(diff(y(x), x) = (x + y(x))^4,y(x), singsol=all)
 

\[ \text {Expression too large to display} \]

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 175

DSolve[D[y[x],x] == (x + y[x])^4,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {1}{x^4+4 K[2] x^3+6 K[2]^2 x^2+4 K[2]^3 x+K[2]^4+1}-\int _1^x-\frac {4 K[1]^3+12 K[2] K[1]^2+12 K[2]^2 K[1]+4 K[2]^3}{\left (K[1]^4+4 K[2] K[1]^3+6 K[2]^2 K[1]^2+4 K[2]^3 K[1]+K[2]^4+1\right )^2}dK[1]\right )dK[2]+\int _1^x\left (\frac {1}{K[1]^4+4 y(x) K[1]^3+6 y(x)^2 K[1]^2+4 y(x)^3 K[1]+y(x)^4+1}-1\right )dK[1]=c_1,y(x)\right ] \]