[" 7.A ctery,and y_2 "" are two different solutions of the equation "y'+P(x)" ."y=Q(x)" ."],[" Such that the linear combination "alpha y_(1)+beta y_(2)" is also solution of given differential equation.Then value of "],[alpha+beta" is "]

Let y_1 and y_2 be two different solutions of the differential equation dy/dx+P(x)*y=Q(x) .Answer the question:If alphay_1+betay_2 is a solution of the given differential equation then alpha+beta is (A) 0 (B) 1 (C) -1 (D) none of these

Let y_(1) and y_(2) be two different solutions of the equation (dy)/(dx)+P(x).y=Q(x) . Then alphay_(1)+betay_(2) will be solution of the given equation if alpha + beta=……………….

Let y_(1) and y_(2) be two different solutions of the equation (dy)/(dx)+P(x).y=Q(x) . Then alphay_(1)+betay_(2) will be solution of the given equation if alpha + beta=……………….

Let y_(1) and y_(2) be two different solutions of the equation (dy)/(dx)+P(x).y=Q(x) . Then alphay_(1)+betay_(2) will be solution of the given equation if alpha + beta=……………….

Let y_(1) and y_(2) be the two solutions of the differential equation (dy)/(dx)+Py=Q , where P and Q are functions of x, Statement-1: The linear combination ay_(1)+by_(2) will be a solution of the differential equation, if a+b=1 . Statement-2 : The general solution of the differential equation is y=y_(1)+C(y_(1)-y_(2)) .

Let y_(1) and y_(2) be the two solutions of the differential equation (dy)/(dx)+Py=Q , where P and Q are functions of x, Statement-1: The linear combination ay_(1)+by_(2) will be a solution of the differential equation, if a+b=1 . Statement-2 : The general solution of the differential equation is y=y_(1)+C(y_(1)-y_(2)) .

If x=2alpha+1\ a n d\ y=alpha-1 is a solution of the equation 2x-3y+5=0 , find the value of alpha

If x=2alpha+1\ a n d\ y=alpha-1 is a solution of the equation 2x-3y+5=0 , find the value of alpha

Consider the differential equation. Dy/dx +P(x)y = Q(x) (i) If two particular solutions of given equation u(x) and v(x) are known, find the general solution of the same equation in terms of u(x) and v(x). (ii) If alpha and beta are constants such that the linear combinations alpha.u(x) + beta.v(x) is a solution of the given equation, find the relation between alpha and beta . (iii) If w(x) is the third particular solution different from u(x) and v(x) then find the ratio v(x) u(x)/w(x)-u(x)

If alpha and beta are the roots of the quadratic equation y^2-2y-7=0, find the values of alpha^2+ beta^2