Question

Consider the differential equation, L[y] = y'' + p(t)y' + q(t)y = 0, (1) whose coefficients p and q are continuous on some open interval I. Choose some point t0 in I. Let y1 be the solution of equation (1) that also satisfies the initial conditions y(t0) = 1, y'(t0) = 0, and let y2 be the solution of equation (1) that satisfies the initial conditions y(t0) = 0, y'(t0) = 1. Then y1 and y2 form a fundamental set of solutions of equation (1). Find the fundamental set of solutions specified by the theorem above for the given differential equation and initial point. y'' + 6y' − 7y = 0, t0 = 0 y1(t) = Incorrect: Your answer is incorrect. y2(t) = Incorrect: Your answer is incorrect.

3. -12 points BoyceDIfiEQ10 320 Consider the differential equation, whose coefficients ρ and q are continuous on some open interval I. Choose some point to in 1. Let yl be the solution of equation (1) that also satisfies the initial conditions and let y2 be the solution of equation (1) that satisfles the initial condition:s Then y1 and y2 form a fundamental set of solutions of equation (1) Ly]- yp(t)yq(t)y y(to)-1, yto)0, y(to) = 0, y"(to) = 1. 0, ) Find the fundamental set of solutions specified by the theorem above for the given differential equation and initial point. vI(t) y2(t) = Additional Materials eBook Submit Answer Save Progress Practice Another Version

Answer 1

Given hat -O G. value. Substitute