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Question: just need help with question 23...

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Just need help with question 23
22. Recall that a linear equation is called homogeneso 0, i.e., if if Q(x) it can be written as dr + P(a)y (a) Show that y 0 is a solution (called the trivial s50nstant, then y (b) Show that if y = yi(x) s a solution and k is a co kyi (z) is also a solution. (c) Show that if y-y1(x) and y = y2(x) are solutions, y2(x) is a solution. then y = yı (x) + dy dr r equation 23. (a) If y- yi() satisfies the homogeneous linear equation + P(x) y = 0 and y2(x) satisfies the nonhomogeneous linear equationdar P(z)y(x), show that y y(x) +y2(x) is a solution to the non- dy dx homogeneous linear equation dy d Pa)y (). (b) Show that if y y() is a solution of dP)y(x), and y y2(x) is a solution of dy + P(zh-q(z), then y m(x) + y2(x) is dy + P(x) y = q(x) + r(z) ryT(), an a solution of
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