Differential Equations
Linear ODE; inverse function area
Grade Class 12
Question:
Curve $y=f(x)$ through origin satisfies $\dfrac{7dy}{dx}+\dfrac{28x^3y}{1+x^4}=\dfrac{40x^4}{1+x^4}$. If area enclosed by $y=f^{-1}(x)$, x-axis, and $x=4/7$ in 1st quadrant is $A$, then $42A$ is
Step-by-Step Solution
Key Concept: Linear ODE with IF$=(1+x^4)^7$. Solve to get $f(x)$, then use area of $f^{-1}(x)=$ (area under $f(x)$) swap formula: $42\cdot A=6$.
$42A=6$.
Correct Answer: 3