8. Solve a' = (t + x)2 by substituting y = t + x. 9. Find the general solution to the differential equation x' = ax + b,

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8 Solve A T X 2 By Substituting Y T X 9 Find The General Solution To The Differential Equation X Ax B 1 (39.25 KiB) Viewed 50 times

8. Solve a' = (t + x)2 by substituting y = t + x. 9. Find the general solution to the differential equation x' = ax + b, where a and b are constants, first by separation of variables, and second by inte- grating factors. 10. Find the general solution to the DE a' = px +q(t), where p is constant. Then find the solution satisfying r(to) = xo. 11. Consider the linear differential equation r'+p(t)x= q(t), and let x₁ = x₁(t) and x2 = x₂(t) be solutions. (a) Show that the sum r(t) = x₁(t) + x₂(t) is a solution if, and only if, q(t) = 0. (b) If x₁ = x₁(t) is a solution to x' + p(t)x= 0 and 2 = x2(t) is a solution to r' + p(t)x= q(t), show that x(t) = x₁(t) + x₂(t) is a solution to x' + p(t)x= q(t).