Advanced Math Archive: Questions from August 02, 2023
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7) Find the IVP solution for \( \left(y^{2} \cos x-3 x^{2} y-2 x\right) d x+\left(2 y \sin x-x^{3}+\ln y\right) d y=0 \) given \( y(0)=c \)2 answers -
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EXTRA CREDIT 1: Solve \( \sec ^{2} y \frac{d y}{d x}+\frac{1}{2 \sqrt{x+1}} \tan y=\frac{1}{2 \sqrt{x+1}} \). EXTRA CREDIT 2: Solve \( y^{\prime}=\frac{2 x y e^{(x / y)^{2}}}{y^{2}+y^{2} e^{(x / y)^{22 answers -
Solve the IVP using Laplace Transform. Please show all work
\( y^{\prime \prime}+y=\sum_{k=1}^{\infty} \delta(t-2 k \pi), \quad y(0)=0, \quad y^{\prime}(0)=1 \)0 answers -
Problem 5 (18 points). Solve the following IVP: y" - 2y' +y = 3t+et, y(0) = 1, y'(0) = 1.
Problem 5 (18 points). Solve the following IVP: \[ y^{\prime \prime}-2 y^{\prime}+y=3 t+e^{t}, \quad y(0)=1, \quad y^{\prime}(0)=1 . \]2 answers -
Solve the DE: (3x^2y + cosx)dx + (x^3 + e^y)dy = 0
2. Solve the DE: \[ \left(3 x^{2} y+\cos x\right) d x+\left(x^{3}+e^{y}\right) d y=0 \]2 answers