WBJEE · Maths · Differential Equations
Integrating Factor (I.F.) of the defferential equation
\(\frac{d y}{d x}-\frac{3 x^2 y}{1+x^3}=\frac{\sin ^2(x)}{1+x} \text { is }\)
- A \(\mathrm{e}^{1+\mathrm{x}^3}\)
- B \(\log \left(1+x^3\right)\)
- C \(1+x^3\)
- D \(\frac{1}{1+x^3}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{1+x^3}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {Hints: If } e^{\int p d x}=e^{-\int \frac{3 x^2 d x}{1+x^3}}=e^{-\log \left(1+x^3\right)}=e^{\log \left(1+x^3\right)^{-1}} \\ & =\left(1+x^3\right)^{-1}=\frac{1}{1+x^3} \end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(A=\left(\begin{array}{cc}3 & x-1 \\ 2 x+3 & x+2\end{array}\right)\) is a symmetric matrix, then the value of \(x\) isWBJEE 2011 Easy
- If the algebraic sum of the distances from the points \((2,0),(0,2)\) and \((1,1)\) to a variable straight line be zero, then the line passes through the fixed pointWBJEE 2022 Medium
- If \(z=\sin \theta-i \cos \theta,\) then for any integer \(n\)WBJEE 2016 Easy
- Number of points having distance \(\sqrt{5}\) fron the straight line \(x-2 y+1=0\) and a distance \(\sqrt{13}\) from the line \(2 x+3 y-1=0,\) isWBJEE 2015 Easy
- Let \(P(4,3)\) be a point on the hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=\mathrm{1}\). If the normal at \(P\) intersects the \(X\) -axis at (16,0) , then the eccentricity of the hyperbola isWBJEE 2019 Medium
- If the tangent to the curve \(y^{2}=x^{3}\) at \(\left(m^{2}, m^{3}\right)\) is also a normal to the curve at \(\left(M^{2}, M^{3}\right)\), then the value of \(m M\) isWBJEE 2020 Medium
More PYQs from WBJEE
-
Two wires \(A\) and \(B\) of same length are made of same material. Load \((F)\) vs. elongation \((x)\) graph for these two wires is shown in the figure. Then which of the following statement(s) is / are true?WBJEE 2022 Medium - The limit of \(x \sin \left(e^{\frac{1}{x}}\right)\) as \(x \rightarrow 0\)WBJEE 2013 Easy
- Five numbers are in AP with common difference \(\neq 0 .\) If the 1 st, 3 rd and 4 th terms are in GP, thenWBJEE 2013 Easy
- A bullet is fired with a velocity u making an angle of \(60^{\circ}\) with the horizontal plane. The horizontal component o the velocity of the bullet when it reaches the maximum height isWBJEE 2009 Medium
- For the reaction \(A+2 B \longrightarrow C\), the reaction rate is doubled, if the concentration of \(A\) is doubled. The rate is increased by four times When concentrations of both \(A\) and \(B\) are increased by four limes. The order of the reaction isWBJEE 2015 Easy
- Solution of \((x+y)^{2} \frac{d y}{d x}=a^{2}\) ('a' being a constant) isWBJEE 2017 Medium