Differential equation Exercise (with solution)
[latex]
\[
\textbf{Question #1 Solve the Differential Equation:} \quad x \frac{dy}{dx} = 4y
\] Solution
\[
\textbf{Given the Differential Equation:} \quad x \frac{d^2y}{dx^2} = 2xy + 3y + 4
\] Solution
\[
\textbf{Question #2 Solve the following differential equation:}
\]
\[
x \cdot 4y^3 \, dx + x \cdot 6y^5 \, dy = 0
\]
\[
\textbf{Question #3 Solve the following differential equation:}
\] Solution
\[
\textbf{Question #4 Solve the following differential equation:}
\]
\[
x \cdot 4y^3 \, dx + x \cdot 6y^5 \, dy = 0
\]
\[
\textbf{Question #5 Solve the differential equation:} \quad x \, dx + 2xy \, dy = 0
\] Solution
\[
\textbf{Question #6: Solve the differential equation:} \quad x \, dx + y – 2x \, dy = 0
\] Solution
\[
\textbf{Question #7: Solve the differential equation:} \quad x \frac{dy}{dx} = 2y
\] Solution
\[
\textbf{Question #8: Solve the differential equation:} \quad x \, dy = y \, dx
\] Solution
\[
\textbf{Question #9: Solve the differential equation:} \quad x^2 y + 1 \, dx + y^2 x + 1 \, dy = 0
\] Solution
\[
\textbf{Question #10: Solve the differential equation:} \quad xy + 4xy \, dx + x + 5xy \, dy = 0
\] Solution
\[
\textbf{Question #11 Solve the differential equation:} \quad xy + 4xy \, dx + x + 5xy \, dy = 0
\] Solution
\[
\textbf{Question #12 Solve the differential equation:} \quad x^2 y^2 \, dx – 2xy \, dy = 0
\] Solution
\[
\textbf{Question #13 Solve the differential equation:} \quad y” = 16y
\] Solution
\[
\textbf{Question #14 Solve the differential equation:} \quad y^2 + 2xy \, dx + x^2 \, dy = 0
\] Solution
\[
\textbf{Question #15 Solve the equation:} \quad y^2 x^2 \frac{dy}{dx} = x y \frac{dy}{dx}
\] Solution
\[
\textbf{Question #16 Solve the homogeneous equation:} \quad y^2 x \, dx + x^2 \, dy = 0
\] Solution
\[
\textbf{Question #17 Solve the differential equation:} \quad \frac{dy}{dx} = xy + 1
\] Solution
\[
\textbf{Question #18 Solve the differential equation:} \quad \frac{dy}{dx} = 2(xy + 1)
\] Solution