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Separable equation for integration.
", "licence": "All rights reserved"}, "statement": "The following first order differential equation is given.
\n\n$\\frac{dy}{dx} = \\frac{x+\\var{a}}{\\var{b}y}$, where $y=\\var{c}$ when $x=0$
", "advice": "$\\frac{dy}{dx} = \\frac{x+\\var{a}}{\\var{b}y}$, where $y=\\var{c}$ when $x=0$
\nSeparate the variables
\n\\[ \\var{b}y.dy = (x+\\var{a}).dx \\]
\nIntegrate each side
\n\\[ \\var{b}\\int{y.dy} = \\int{(x+\\var{a})}.dx \\]
\n\\[\\frac{\\var{b} y^2}{2}=\\frac{x^2}{2}+\\var{a}x+C \\] ...general solution
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\n$\\frac{dy}{dx} = \\frac{x+\\var{a}}{\\var{b}y}$
\nEnter values as integers or fractions. Use C as the constant of integration.
\n$y =$ [[0]]
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\n\\[y =( {\\var{-a+1}}(\\frac{x^{2}}{2} + C))^{\\frac{1}{\\var{-a+1}}}\\]
\nEvaluate the constant of integration, C, for the initial conditions $y=\\var{b}$ when $x=0$. Input values as decimal.
\n$C=$ [[0]]
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\n\\[C=\\var{Cint}\\]
\nSub this back into the general solution and write the particular solution in terms of y.
\n$y =$ [[0]]
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