a) K-3 Solve the differential equation a = kyx using the method of separation of variables. dy dx b) 3 Discuss the difference between the direction fields of the differential equations dy=kyx and dy dx = = -kyx. How the sign of the coefficient affects the solution curves. A racquetball is hit straight upward with an initial velocity of v₁ = km/s. The mass of a racquetball is m=0.05kg. Air resistance acts on the ball with a force numerically equal to Air resistance acts on the ball with a force numerically equal to 0.5v, where v represents the velocity of the ball at time t. To find the velocity of the ball as a function of time and evaluate time for the ball to reach its maximum height w can solve initial value problem using the firs order linear DE such as dv m dt == −0.5v — m(9.8), v₁ = k ← k=3 Rewrite the equation as a standard form of a linear DE. Find the integration factor. d) k= 3 Sketch the direction field of the equation from part c) both manually and by using software. Explain the relation between the solution curves and the direction field. K= 3 Find the velocity of the ball as a function of time. How long does it take for the ball to reach its maximum height?

Plz help with this differential equations

product rule 3. Use the substitution up to solve the differential equation xy' + 5y = 3ay

Hi, can I get some help with this differential equations problem? An object weighting 16 pounds is attached to a string, thereby stretching the spring 12 inches. The object is then displaced an additional 6 inches and released at t = 0. The medium exerts a resistance of 8 pounds when the object has a velocity of 2 feet per second. Find the object's displacement, y(t), in feet after t seconds.