Homogeneous Equations: JEE Main previous year questions.

• Substitution y = vxOpenRepeated10 · 45%45%6/824
  • 5 Apr ’26 S1 · Q25
    Let $y = y(x)$ be the solution of the differential equation…

    hardNumerical value

  • 9 Apr ’24 S1 · Q10
    The solution of the differential equation $(x^2+y^2)dx-5xy\,dy=0$, $y(1)=0$, is :

    mediumSingle correctAsked the year before

  • 10 Apr ’23 S1 · Q10
    The slope of tangent at any point $(x,y)$ on a curve $y=y(x)$ is $\frac{x^2+y^2}{2xy}$, $x>0$. If $y(2)=0$, then a value of $y(8)$ is

    mediumSingle correctAsked the year before

  • 25 Jul ’22 S2 · Q25
    Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=\frac{4y^3+2yx^2}{3xy^2+x^3},\ y(1)=1$. If for some…

    mediumNumerical valueAsked the year before

  • 28 Jul ’22 S1 · Q1
    Let the solution curve of the differential equation $x\,dy=\left(\sqrt{x^2+y^2}+y\right)dx,\ x>0$, intersect the line $x=1$ at $y=0$ and…

    mediumSingle correctAsked the year before

  • 28 Jun ’22 S1 · Q10
    Let the solution curve $y=y(x)$ of the differential equation…

    hardSingle correctAsked the year before

  • 29 Jun ’22 S1 · Q2
    Let the solution curve of the differential equation $x\frac{dy}{dx} - y = \sqrt{y^2 + 16x^2}$, $y(1) = 3$ be $y = y(x)$. Then $y(2)$ is…

    mediumSingle correctAsked the year before

  • 18 Mar ’21 S2 · Q86
    Let $y=y(x)$ be the solution of the differential equation $x\,dy-y\,dx=\sqrt{(x^2-y^2)}\,dx$, $x\ge1$, with $y(1)=0$. If the area bounded…

    hardNumerical valueAsked the year before

  • 9 Jan ’20 S2 · Q64
    If $\frac{dy}{dx}=\frac{xy}{x^2+y^2}$; $y(1)=1$; then a value of $x$ satisfying $y(x)=e$ is :

    mediumSingle correctNew idea

  • 2 Sep ’20 S2 · Q63
    If a curve $y=f(x)$, passing through the point $(1,\,2)$, is the solution of the differential equation, $2x^2\,dy=(2xy+y^2)\,dx$, then…

    mediumSingle correctNew idea

• Alternative Substitution x = vyOpenRepeated2 · 9%9%2/8
• Homogeneous Equations with Transcendental FunctionsOpenRepeated2 · 9%9%2/8
• Identifying Equations Reducible to Homogeneous FormOpen2 · 9%9%1/82
• Recognizing Exact Differentials in Homogeneous FormsOpenRepeated2 · 9%9%2/8
• Domain Restrictions from Initial Value ProblemsOpen1 · 5%5%1/8
• Finding Particular SolutionsOpen1 · 5%5%1/8
• Identifying Homogeneous FunctionsOpen1 · 5%5%1/8
• Shift of Origin Method for Reducible EquationsOpen1 · 5%5%1/8

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.