Practice Final Exam haileygray Project2 - Goog ses/553449/quizzes/1547338/take Question 1 Solve the linear initial value problem. \[ x \frac{d y}{d x}-y=x^{3} e^{x}, y(1)=e \] ? \( y(x)=x^{2} e^{x}-2 x e^{x}+2 e^{x} \) ? \( y(x)=x^{3} e^{x}-2 x^{2} e^{x}+2 x e^{x} \) ? \( y(x)=x-2 e^{x}+\frac{2}{x} e^{x}+e-1 \) ? \( y(x)=x^{2} e^{x}-x e^{x}+e x \) ? \( y(x)=\frac{1}{4} x^{4} e^{x}+\frac{3}{4} e^{x} \) Question 2 Find the implicit general solution to the given separable differential equation. \[ \left(x^{3}+7 x^{3} y^{4}\right) d x+e^{x^{4}} y^{3} d y=0 \] ? \[ \ln \left(1+7 y^{4}\right)-\frac{1}{}=C \] Search
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Q1: y''' - 6y'' + 11y' - 6y = 0 differential equation does have 2 solutions y1(x) = e^x and y2(x) = e^(2x). Investigate the given equation: y(x) = c1e^x + c2e^(2x), as the general solution of the differential equation above. Q2: (3x^2y + 1/y) dx - (x/y^2) dy = 0, y(2) = 1. Find the solution of the differential equation for the given initial value.
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