Pregunta: 1. Solve the following differential equations: (a) y ′ + y = sin(ex ) (b) (1 + t) du/dt + u = 1 + t, t > 0 (c) t ln t dr/dt + r = tet (d) x dy/dx − 4y = x4ex 2. Solve the following initial value problems: (a) t3 dy/dt + 3t2 y = cos t, y(π) = 0 (b) xy′ = y + x2 sin x, y(π) = 0 (c) (x2 + 1)dy/dx + 3x(y − 1) = 0, y(0) = 2 4. Solve the following differential

1. Solve the following differential equations: (a) y ′ + y = sin(e^x ) (b) (1 + t) du/dt + u = 1 + t, t > 0 (c) t ln t dr/dt + r = te^t (d) x dy/dx − 4y = x⁴e^x

2. Solve the following initial value problems: (a) t³ dy/dt + 3t² y = cos t, y(π) = 0 (b) xy′ = y + x² sin x, y(π) = 0 (c) (x² + 1)dy/dx + 3x(y − 1) = 0, y(0) = 2

4. Solve the following differential equations: (a) xy′ + y = −xy² (b) y ′ + 2/x * y = y³ /x²