Mathematics

This is a separable differential equation where the key insight is recognizing that the numerator is almost the derivative of the denominator. Notice that if you differentiate $x^3 + 4x$, you get $3x^2 + 4$—exactly your numerator! This means you can integrate both sides by recognizing the natural logarithm pattern: $\int \frac{d(u)}{u} = \ln|u| + C$. Once you find the general solution, use the initial condition $y(1) = 0$ to pin down the constant.

This is a separable differential equation where the key insight is recognizing that the numerator is almost the derivative of the denominator. Notice that if you differentiate $x^3 + 4x$, you get $3x^2 + 4$—exactly your numerator! This means you can integrate both sides by recognizing the natural logarithm pattern: $\int \frac{d(u)}{u} = \ln|u| + C$. Once you find the general solution, use the initial condition $y(1) = 0$ to pin down the constant.