(Solved): (1 point) In this problem you will solve the non-homogeneous differential equation y+121y=se ...

(1 point) In this problem you will solve the non-homogeneous differential equation $$y^{??}+121y={\sec }^2(11x)$$ (1) Let $$C_1$$ and $$C_2$$ be arbitrary constants. The general solution to the related homogeneous differential equation $$y^{??}+121y=0$$ is the function $$y_h(x)=C_1{y}_1(x)+C_2{y}_2(x)=C_1+C_2$$ NOTE: The order in which you enter the answers is important; that is, $$C_{1}f(x)+C_{2}g(x)?=C_{1}g(x)+C_{2}f(x)$$. (2) The particular solution $$y_p(x)$$ to the differential equation $$y^{??}+121y={\sec }^2(11x)$$ is of the form $$y_p(x)=y_1(x)u_1(x)+y_2(x)u_2(x)$$ where $$u_1^{?}(x)=$$ and $$u_2^{?}(x)=$$ (3) It follows that $$u_1(x)=$$ and $$u_2(x)=$$ ; thus $$y_p(x)=$$ (4) The most general solution to the non-homogeneous differential equation $$y^{??}+121y={\sec }^2(11x)$$ is $$y=C_1$$ $$+C_2$$ $$+$$