Painlevé Transcendents - 32.3 Graphics

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
32.3.E2	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}u}{{\mathrm{d}x}^{2}}=3u^{5}+2xu^{3}+\left(\tfrac{1}{4}x^{2}-\nu-\tfrac{1}{2}\right)u}}$ \deriv[2]{u}{x} = 3u^{5}+2xu^{3}+\left(\tfrac{1}{4}x^{2}-\nu-\tfrac{1}{2}\right)u		diff(u, [x$(2)]) = 3*(u)^(5)+ 2*x*(u)^(3)+((1)/(4)*(x)^(2)- nu -(1)/(2))*u	D[u, {x, 2}] == 3*(u)^(5)+ 2*x*(u)^(3)+(Divide[1,4]*(x)^(2)- \[Nu]-Divide[1,2])*u	Failure	Failure	ExpandFailed [300 / 300] Result: 3.043949625-3.665224602*I Test Values: {nu = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, x = 3/2} Result: 3.476962328-1.415224600*I Test Values: {nu = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, x = 1/2} ... skip entries to safe data	ExpandFailed [300 / 300] Result: Complex[3.043949623616789, -3.6652245962155616] Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.67792421983235, -4.031249999999999] Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
32.3.E4	${\displaystyle{\displaystyle w(x)=2\sqrt{2}u_{k}^{2}(\sqrt{2}x,\nu)}}$ w(x) = 2\sqrt{2}u_{k}^{2}(\sqrt{2}x,\nu)		w(x) = 2*sqrt(2)*(u[k])^(2)(sqrt(2)*x , nu)	w[x] == 2*Sqrt[2]*(Subscript[u, k])^(2)[Sqrt[2]*x , \[Nu]]	Skipped - no semantic math	Skipped - no semantic math	-	-
32.3.E6	${\displaystyle{\displaystyle u^{2}=-\tfrac{1}{3}x+\tfrac{1}{6}\sqrt{x^{2}+12\nu+6}}}$ u^{2} = -\tfrac{1}{3}x+\tfrac{1}{6}\sqrt{x^{2}+12\nu+6}		(u)^(2) = -(1)/(3)*x +(1)/(6)*sqrt((x)^(2)+ 12*nu + 6)	(u)^(2) == -Divide[1,3]*x +Divide[1,6]*Sqrt[(x)^(2)+ 12*\[Nu]+ 6]	Skipped - no semantic math	Skipped - no semantic math	-	-