AP EAMCET · Maths · Differential Equations
\(a, b, c, d\) are real numbers. The general solution of \(\frac{d y}{d x}=\frac{a x+b}{c y+d}\) represents a family of straight lines, when
- A \(a=c=0\), and \(b^2+d^2 \neq 0\)
- B \(a \neq 0, c=0\) or \(a=0, c \neq 0\)
- C \(b d=0, a \neq 0, c \neq 0\)
- D \(b+d=0, a+c=0\)
Answer & Solution
Correct Answer
(A) \(a=c=0\), and \(b^2+d^2 \neq 0\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \frac{d y}{d x}=\frac{a x+b}{c y+d} \\ & \qquad \int(c y+d) d y=\int(a x+b) d x \\ & \frac{c y^2}{2}+d y=\frac{a x^2}{2}+b x+k \text {, where } k \text { is constant of } \\ & \text { integration. } \\ & \text { For a family a straight line, } c=a=0…
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