query: Convergence of the solution and their derivative of the equation $y''+y'+y^{3}=0$.
positive_passages.docid: 152143
positive_passages.text: Limits for the solution of the non-linear ODE
negative_passages.docid: 147299
negative_passages.text: Prove that $g(x,y) = \frac{x^3y}{x^2+y^2}$ with $g(0,0)=0$ is continuous
negative_passages.docid: 67158
negative_passages.text: Solve $y'-\int_0^xy(t)dt=2$
negative_passages.docid: 106038
negative_passages.text: Burgers' equation $u_y + uu_x = 0$ with $u(x,0)=-x$
negative_passages.docid: 111812
negative_passages.text: Uniform Convergence of Difference Quotients to Partial Derivative
negative_passages.docid: 16970
negative_passages.text: Convergence of $\sqrt{n}x_{n}$ where $x_{n+1} = \sin(x_{n})$
negative_passages.docid: 43537
negative_passages.text: How can $x^2y''-3xy'+3y=0$ be solved?
negative_passages.docid: 150057
negative_passages.text: Approximating a three-times differentiable function by a linear combination of derivatives
negative_passages.docid: 91023
negative_passages.text: Limit of $y$ if limit of $y+y'$ goes to $0$?
negative_passages.docid: 35885
negative_passages.text: Monotonicity and convergence of the sequence $a_n=\sum_{k=1}^{n}\frac{1}{k+n}$
negative_passages.docid: 148443
negative_passages.text: convergence of infinite sum of integer values of integrable function
negative_passages.docid: 29810
negative_passages.text: Derivation of a generalization of Mertens' Third Theorem.
negative_passages.docid: 153942
negative_passages.text: Solution of functional equation $f(x+y)=f(x)+f(y)+y\sqrt{f(x)}$
negative_passages.docid: 71465
negative_passages.text: solution of $y' = \exp \left(-\frac yx\right) + \frac yx$
negative_passages.docid: 44261
negative_passages.text: Convergence of $\sum^\infty_{n=1} \ln(1+\frac 1 {2^n})$
negative_passages.docid: 72604
negative_passages.text: The differential equation $y''-q(x)y=0.$
negative_passages.docid: 14517
negative_passages.text: Existence of solutions of the equation with a limit.